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Computer Algebra in Scientific Computing [[electronic resource] ] : 20th International Workshop, CASC 2018, Lille, France, September 17–21, 2018, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing [[electronic resource] ] : 20th International Workshop, CASC 2018, Lille, France, September 17–21, 2018, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (XIII, 379 p. 54 illus.) |
| Disciplina | 005.3 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Algorithms
Computer science—Mathematics Computers, Special purpose Computer systems Logic design Computer science Mathematics of Computing Special Purpose and Application-Based Systems Computer System Implementation Logic Design Computer Science Logic and Foundations of Programming |
| ISBN | 3-319-99639-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Proof-of-Work Certificates that Can Be Efficiently Computed in the Cloud (Invited Talk) -- On Unimodular Matrices of Difference Operators -- Sparse Polynomial Arithmetic with the BPAS Library -- Computation of Pommaret Bases Using Syzygies -- A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations -- Symbolic-Numeric Methods for Nonlinear Integro-Differential Modeling -- A Continuation Method for Visualizing Planar Real Algebraic Curves with Singularities -- From Exponential Analysis to Padé Approximation and Tensor Decomposition, in One and More Dimensions -- Symbolic Algorithm for Generating the Orthonormal Bargmann-Moshinsky Basis for SU(3) Group -- About Some Drinfel'd Associators -- On a Polytime Factorization Algorithm for Multilinear Polynomials over F2 -- Tropical Newton-Puiseux Polynomials -- Orthogonal Tropical Linear Prevarieties -- Symbolic-Numerical Algorithms for Solving Elliptic Boundary-Value Problems Using Multivariate Simplex Lagrange Elements -- Symbolic-Numeric Simulation of Satellite Dynamics with Aerodynamic Attitude Control System -- Finding Multiple Solutions in Nonlinear Integer Programming with Algebraic Test-Sets -- Positive Solutions of Systems of Signed Parametric Polynomial Inequalities -- Qualitative Analysis of a Dynamical System with Irrational First Integrals -- Effective Localization Using Double Ideal Quotient and Its Implementation -- A Purely Functional Computer Algebra System Embedded in Haskell -- Splitting Permutation Representations of Finite Groups by Polynomial Algebra Methods -- Factoring Multivariate Polynomials with Many Factors and Huge Coefficients -- Beyond the First Class of Analytic Complexity -- A Theory and an Algorithm for Computing Sparse Multivariate Polynomial Remainder Sequence -- A Blackbox Polynomial System Solver on Parallel Shared Memory Computers. |
| Record Nr. | UNISA-996466360403316 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Computer Algebra in Scientific Computing : 20th International Workshop, CASC 2018, Lille, France, September 17–21, 2018, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing : 20th International Workshop, CASC 2018, Lille, France, September 17–21, 2018, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (XIII, 379 p. 54 illus.) |
| Disciplina | 005.3 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Algorithms
Computer science—Mathematics Computers, Special purpose Computer systems Logic design Computer science Mathematics of Computing Special Purpose and Application-Based Systems Computer System Implementation Logic Design Computer Science Logic and Foundations of Programming |
| ISBN | 3-319-99639-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Proof-of-Work Certificates that Can Be Efficiently Computed in the Cloud (Invited Talk) -- On Unimodular Matrices of Difference Operators -- Sparse Polynomial Arithmetic with the BPAS Library -- Computation of Pommaret Bases Using Syzygies -- A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations -- Symbolic-Numeric Methods for Nonlinear Integro-Differential Modeling -- A Continuation Method for Visualizing Planar Real Algebraic Curves with Singularities -- From Exponential Analysis to Padé Approximation and Tensor Decomposition, in One and More Dimensions -- Symbolic Algorithm for Generating the Orthonormal Bargmann-Moshinsky Basis for SU(3) Group -- About Some Drinfel'd Associators -- On a Polytime Factorization Algorithm for Multilinear Polynomials over F2 -- Tropical Newton-Puiseux Polynomials -- Orthogonal Tropical Linear Prevarieties -- Symbolic-Numerical Algorithms for Solving Elliptic Boundary-Value Problems Using Multivariate Simplex Lagrange Elements -- Symbolic-Numeric Simulation of Satellite Dynamics with Aerodynamic Attitude Control System -- Finding Multiple Solutions in Nonlinear Integer Programming with Algebraic Test-Sets -- Positive Solutions of Systems of Signed Parametric Polynomial Inequalities -- Qualitative Analysis of a Dynamical System with Irrational First Integrals -- Effective Localization Using Double Ideal Quotient and Its Implementation -- A Purely Functional Computer Algebra System Embedded in Haskell -- Splitting Permutation Representations of Finite Groups by Polynomial Algebra Methods -- Factoring Multivariate Polynomials with Many Factors and Huge Coefficients -- Beyond the First Class of Analytic Complexity -- A Theory and an Algorithm for Computing Sparse Multivariate Polynomial Remainder Sequence -- A Blackbox Polynomial System Solver on Parallel Shared Memory Computers. |
| Record Nr. | UNINA-9910349411103321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer Algebra in Scientific Computing [[electronic resource] ] : 19th International Workshop, CASC 2017, Beijing, China, September 18-22, 2017, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing [[electronic resource] ] : 19th International Workshop, CASC 2017, Beijing, China, September 18-22, 2017, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
| Descrizione fisica | 1 online resource (XIII, 407 p. 75 illus.) |
| Disciplina | 004.0151 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Algorithms
Computer science—Mathematics Computers, Special purpose Electronic data processing—Management Software engineering Computer science Mathematics of Computing Special Purpose and Application-Based Systems IT Operations Software Engineering Computer Science Logic and Foundations of Programming |
| ISBN | 3-319-66320-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Organization -- Contents -- Linear Differential Systems with Infinite Power Series Coefficients (Invited Talk) -- 1 Introduction -- 2 Algorithmic Representation -- 2.1 Computable Infinite Power Series in the Role of Coefficients of Linear Differential Systems -- 2.2 Procedures for Constructing Local Solutions -- 3 Approximate (Truncated) Representation -- 3.1 Strongly Non-singular Matrices -- 3.2 When only a Truncated System Is Known -- 4 The Width -- References -- On the Asymptotic Stability of a Satellite with a Gravitational Stabilizer -- 1 Introduction -- 2 Description and Construction of a Symbolical Model -- 3 Formulation of the Problem -- 4 Regions of System's Instability -- 5 Parametric Analysis of Asymptotic Stability Conditions -- 5.1 Stabilization in the ``Pitch'' Subsystem -- 5.2 Stabilization in the ``Yaw-and-Roll'' Subsystem -- 6 Conclusion -- References -- Sparse Interpolation, the FFT Algorithm and FIR Filters -- 1 Sparse Interpolation -- 2 Divide and Conquer Approach -- 3 The FFT Algorithm -- 4 An Analog Version of the Splitting Technique -- 5 Connection to FIR Filters -- 6 Conclusion -- References -- On New Integrals of the Algaba-Gamero-Garcia System -- 1 Introduction -- 2 Problem Statement -- 3 Necessary Conditions of Local Integrability -- 4 Sufficient Conditions of Integrability -- 5 Case b2=2/3, Subcase 3 a0 - 2 b0 = b(3 a1 - 2 b1) -- 6 Analytical Properties of the Integrals -- 7 Conclusions -- References -- Full Rank Representation of Real Algebraic Sets and Applications -- 1 Introduction -- 2 Full Rank Representation of Real Algebraic Sets -- 3 Compute Full Rank Representation -- 4 Applications on Plotting Singular Plane and Space Curves -- 5 Experimentation -- 6 Conclusion and Future Work -- References -- Certifying Simple Zeros of Over-Determined Polynomial Systems -- 1 Introduction.
2 Preliminaries -- 3 Transforming Over-Determined Polynomial Systems into Square Ones -- 4 Certifying Simple Zeros of Over-Determined Systems -- References -- Decomposing Polynomial Sets Simultaneously into Gröbner Bases and Normal Triangular Sets -- 1 Introduction -- 2 Preliminaries -- 2.1 Triangular Set and Triangular Decomposition -- 2.2 Gröbner Basis and W-Characteristic Set -- 2.3 (Strong) Characteristic Decomposition and Characterizable Gröbner Basis -- 3 Algorithm for (Strong) Characteristic Decomposition -- 3.1 Algorithm to Handle the Variable Ordering Condition -- 3.2 Algorithms for Characteristic Decomposition -- 3.3 Algorithm for Strong Characteristic Decomposition -- 3.4 An Illustrative Example -- 4 Implementation and Experimental Results -- References -- Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks -- 1 Introduction -- 2 The Systems for the Case Studies -- 2.1 Biomod-26 -- 2.2 Biomod-28 -- 3 Graph-Theoretical Symbolic Preprocessing -- 4 Determination of Multiple Steady States -- 4.1 Numerical Approach -- 4.2 Symbolic Approach -- 4.3 Comparison -- 4.4 Going Further -- 5 Conclusion and Future Work -- References -- The Polymake Interface in Singular and Its Applications -- 1 Introduction -- 2 An Interface to Polymake -- 3 User Defined Types in Singular: Polyhedral Divisors -- 4 Quasihomogeneous Isolated Hypersurface Singularities -- 4.1 Finding Quasihomogeneous Isolated Hypersurface Singularities -- 4.2 Reconstruction of QHIS from the Milnor Algebra -- References -- Computation of Some Integer Sequences in Maple -- 1 Introduction -- 1.1 Definitions of Numbers -- 2 Stirling Partition Numbers -- 2.1 Sequence Calculation -- 3 Stirling Cycle Numbers -- 3.1 Singleton Computation -- 3.2 A Finite Sum -- 3.3 Sequence Calculation -- 4 Associated Stirling Numbers. 4.1 Singleton Stirling 2-Partition and 2-Cycle -- 4.2 Sequence Calculation of 2-Partition and 2-Cycle Numbers -- 4.3 Singleton Stirling r-Partition and r-Cycle Numbers -- 4.4 Sequence Calculation of r-Partition and r-Cycle Numbers -- 4.5 Implementation in Maple -- 5 A Multiple Threads Approach to Sequence Calculations -- 6 Implementation of Eulerian Numbers -- 6.1 Timings for Eulerian Number Calculations -- References -- Symbolic-Numerical Algorithm for Generating Interpolation Multivariate Hermite Polynomials of High-Accuracy Finite Element Method -- 1 Introduction -- 2 Setting of the Problem -- 3 FEM Calculation Scheme -- 3.1 Lagrange Interpolation Polynomials -- 3.2 Algorithm for Calculating the Basis of Hermite Interpolating Polynomials -- 3.3 Example: HIP for d=2 -- 3.4 Piecewise Polynomial Functions -- 4 Results and Discussion -- 5 Conclusion -- References -- Symbolic-Numerical Algorithms for Solving the Parametric Self-adjoint 2D Elliptic Boundary-Value Problem Using High-Accuracy Finite Element Method -- 1 Introduction -- 2 FEM Algorithm for Solving the Parametric 2D BVP -- 3 Fully Symmetric High-Order Gaussian Quadratures -- 4 The Algorithm for Calculating the Parametric Derivatives of Eigenfunctions and Effective Potentials -- 5 Benchmark Calculations of Helium Atom Ground State -- 6 Conclusion -- References -- A Symbolic Study of the Satellite Dynamics Subject to Damping Torques -- 1 Introduction -- 2 Equations of Motion -- 3 Equilibrium Orientations of Satellite -- 4 Conditions for the Existence of Equilibrium Orientations of the Satellite -- 5 Necessary and Sufficient Conditions of Asymptotic Stability of the Equilibrium Orientations of Satellite -- 6 Conclusion -- References -- Characteristic Set Method for Laurent Differential Polynomial Systems -- 1 Introduction -- 2 Laurent Polynomial Systems -- 2.1 Laurent Regular Chain. 2.2 Characteristic Set Method -- 2.3 Laurent Gröbner Basis and Minimal Decomposition -- 3 Differential Polynomial Systems -- 3.1 Laurent Regular Differential Chains -- 3.2 Decision of Univariate Laurent Regular Differential Polynomial -- References -- Sparse Polynomial Interpolation with Finitely Many Values for the Coefficients -- 1 Introduction -- 2 Univariate Polynomial Interpolation -- 2.1 Sparse Interpolation with Finitely Many Coefficients -- 2.2 The Sparse Interpolation Algorithm -- 2.3 The Rational Number Coefficients Case -- 3 Multivariate Polynomial Sparse Interpolation with Modified Kronecker Substitution -- 3.1 Find a Good Prime -- 3.2 A Deterministic Algorithm -- 3.3 Probabilistic Algorithm -- 4 Experimental Results -- 5 Conclusion -- References -- On Stationary Motions of the Generalized Kowalewski Gyrostat and Their Stability -- 1 Introduction -- 2 Formulation of the Problem -- 3 Finding the Stationary Solutions -- 3.1 Permanent Rotations -- 3.2 Equilibria -- 4 On Invariant Manifolds of Codimension 2 -- 5 On Stability of the Stationary Solutions -- 5.1 On Stability of the Permanent Rotations -- 5.2 On Stability of the Equilibria -- 6 Conclusion -- 7 Appendix -- References -- Computing the Integer Points of a Polyhedron, I: Algorithm -- 1 Introduction -- 2 Polyhedral Sets -- 3 Integer Solutions of Linear Equation Systems -- 4 Integer Solutions of Linear Inequality Systems -- 4.1 Normalization of Linear Inequality Systems -- 4.2 Representing the Integer Points -- 4.3 The IntegerSolve Procedure: Specifications -- 4.4 The DarkShadow Procedure -- 4.5 The GreyShadow Procedure -- 4.6 The IntegerSolve Procedure: Algorithm -- References -- Computing the Integer Points of a Polyhedron, II: Complexity Estimates -- 1 Introduction -- 2 Properties of the Projection of Faces of a Polyhedron -- 3 Complexity Estimates for Fourier-Motzkin Elimination. 4 Proof of Theorem1 -- 5 Experimentation -- References -- Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data -- 1 Problem Formulation -- 2 Non-Linearity of JTF and Numerical Difficulties -- 3 Non-Convexity of JTF -- 4 Numerical Experiments for Fitting Sparse Reduced Data -- 5 Conclusions -- References -- The Convergence Conditions of Interval Newton's Method Based on Point Estimates -- 1 Introduction -- 2 Notation and Preliminaries -- 3 Main Results -- 4 Example -- References -- Normalization of Indexed Differentials Based on Function Distance Invariants -- 1 Introduction -- 2 Indexed Differential Polynomial Ring -- 3 Distances Between Indexed Functions -- 4 Normalization with Respect to Monoterm Symmetries -- 5 Normalization -- References -- Symbolic-Numeric Integration of the Dynamical Cosserat Equations -- 1 Introduction -- 2 Governing Cosserat Equations and the General Solution of Their Kinematic Part -- 3 Symbolic-Numeric Integration Method -- 3.1 Naive Approach: Explicit Numerical Solving -- 3.2 Advanced Approach Based on Exponential Integration -- 4 Numerical Comparison with the Generalized alpha-Method -- 5 Conclusison -- A Generalized alpha-Method -- References -- Algorithms for Zero-Dimensional Ideals Using Linear Recurrent Sequences -- 1 Introduction -- 2 Generalities on Sequences and Their Annihilators -- 3 Computing Annihilators of Sequences -- 3.1 A First Algorithm -- 3.2 An Algorithm Under Genericity Assumptions -- 4 Main Algorithm -- 4.1 Representing Primary Zero-Dimensional Ideals -- 4.2 The Algorithm -- References -- Symbolic-Numerical Analysis of the Relative Equilibria Stability in the Planar Circular Restricted Four-Body Problem -- 1 Introduction -- 2 Equilibrium Solutions -- 3 Stability Analysis in Linear Approximation -- 4 Normalization of the Hamiltonian -- 5 Conclusion -- References. The Method of Collocations and Least Residuals Combining the Integral Form of Collocation Equations and the Matching Differential Relations at the Solution of PDEs. |
| Record Nr. | UNISA-996465568403316 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Computer Algebra in Scientific Computing : 19th International Workshop, CASC 2017, Beijing, China, September 18-22, 2017, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing : 19th International Workshop, CASC 2017, Beijing, China, September 18-22, 2017, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
| Descrizione fisica | 1 online resource (XIII, 407 p. 75 illus.) |
| Disciplina | 004.0151 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Algorithms
Computer science—Mathematics Computers, Special purpose Electronic data processing—Management Software engineering Computer science Mathematics of Computing Special Purpose and Application-Based Systems IT Operations Software Engineering Computer Science Logic and Foundations of Programming |
| ISBN | 3-319-66320-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Organization -- Contents -- Linear Differential Systems with Infinite Power Series Coefficients (Invited Talk) -- 1 Introduction -- 2 Algorithmic Representation -- 2.1 Computable Infinite Power Series in the Role of Coefficients of Linear Differential Systems -- 2.2 Procedures for Constructing Local Solutions -- 3 Approximate (Truncated) Representation -- 3.1 Strongly Non-singular Matrices -- 3.2 When only a Truncated System Is Known -- 4 The Width -- References -- On the Asymptotic Stability of a Satellite with a Gravitational Stabilizer -- 1 Introduction -- 2 Description and Construction of a Symbolical Model -- 3 Formulation of the Problem -- 4 Regions of System's Instability -- 5 Parametric Analysis of Asymptotic Stability Conditions -- 5.1 Stabilization in the ``Pitch'' Subsystem -- 5.2 Stabilization in the ``Yaw-and-Roll'' Subsystem -- 6 Conclusion -- References -- Sparse Interpolation, the FFT Algorithm and FIR Filters -- 1 Sparse Interpolation -- 2 Divide and Conquer Approach -- 3 The FFT Algorithm -- 4 An Analog Version of the Splitting Technique -- 5 Connection to FIR Filters -- 6 Conclusion -- References -- On New Integrals of the Algaba-Gamero-Garcia System -- 1 Introduction -- 2 Problem Statement -- 3 Necessary Conditions of Local Integrability -- 4 Sufficient Conditions of Integrability -- 5 Case b2=2/3, Subcase 3 a0 - 2 b0 = b(3 a1 - 2 b1) -- 6 Analytical Properties of the Integrals -- 7 Conclusions -- References -- Full Rank Representation of Real Algebraic Sets and Applications -- 1 Introduction -- 2 Full Rank Representation of Real Algebraic Sets -- 3 Compute Full Rank Representation -- 4 Applications on Plotting Singular Plane and Space Curves -- 5 Experimentation -- 6 Conclusion and Future Work -- References -- Certifying Simple Zeros of Over-Determined Polynomial Systems -- 1 Introduction.
2 Preliminaries -- 3 Transforming Over-Determined Polynomial Systems into Square Ones -- 4 Certifying Simple Zeros of Over-Determined Systems -- References -- Decomposing Polynomial Sets Simultaneously into Gröbner Bases and Normal Triangular Sets -- 1 Introduction -- 2 Preliminaries -- 2.1 Triangular Set and Triangular Decomposition -- 2.2 Gröbner Basis and W-Characteristic Set -- 2.3 (Strong) Characteristic Decomposition and Characterizable Gröbner Basis -- 3 Algorithm for (Strong) Characteristic Decomposition -- 3.1 Algorithm to Handle the Variable Ordering Condition -- 3.2 Algorithms for Characteristic Decomposition -- 3.3 Algorithm for Strong Characteristic Decomposition -- 3.4 An Illustrative Example -- 4 Implementation and Experimental Results -- References -- Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks -- 1 Introduction -- 2 The Systems for the Case Studies -- 2.1 Biomod-26 -- 2.2 Biomod-28 -- 3 Graph-Theoretical Symbolic Preprocessing -- 4 Determination of Multiple Steady States -- 4.1 Numerical Approach -- 4.2 Symbolic Approach -- 4.3 Comparison -- 4.4 Going Further -- 5 Conclusion and Future Work -- References -- The Polymake Interface in Singular and Its Applications -- 1 Introduction -- 2 An Interface to Polymake -- 3 User Defined Types in Singular: Polyhedral Divisors -- 4 Quasihomogeneous Isolated Hypersurface Singularities -- 4.1 Finding Quasihomogeneous Isolated Hypersurface Singularities -- 4.2 Reconstruction of QHIS from the Milnor Algebra -- References -- Computation of Some Integer Sequences in Maple -- 1 Introduction -- 1.1 Definitions of Numbers -- 2 Stirling Partition Numbers -- 2.1 Sequence Calculation -- 3 Stirling Cycle Numbers -- 3.1 Singleton Computation -- 3.2 A Finite Sum -- 3.3 Sequence Calculation -- 4 Associated Stirling Numbers. 4.1 Singleton Stirling 2-Partition and 2-Cycle -- 4.2 Sequence Calculation of 2-Partition and 2-Cycle Numbers -- 4.3 Singleton Stirling r-Partition and r-Cycle Numbers -- 4.4 Sequence Calculation of r-Partition and r-Cycle Numbers -- 4.5 Implementation in Maple -- 5 A Multiple Threads Approach to Sequence Calculations -- 6 Implementation of Eulerian Numbers -- 6.1 Timings for Eulerian Number Calculations -- References -- Symbolic-Numerical Algorithm for Generating Interpolation Multivariate Hermite Polynomials of High-Accuracy Finite Element Method -- 1 Introduction -- 2 Setting of the Problem -- 3 FEM Calculation Scheme -- 3.1 Lagrange Interpolation Polynomials -- 3.2 Algorithm for Calculating the Basis of Hermite Interpolating Polynomials -- 3.3 Example: HIP for d=2 -- 3.4 Piecewise Polynomial Functions -- 4 Results and Discussion -- 5 Conclusion -- References -- Symbolic-Numerical Algorithms for Solving the Parametric Self-adjoint 2D Elliptic Boundary-Value Problem Using High-Accuracy Finite Element Method -- 1 Introduction -- 2 FEM Algorithm for Solving the Parametric 2D BVP -- 3 Fully Symmetric High-Order Gaussian Quadratures -- 4 The Algorithm for Calculating the Parametric Derivatives of Eigenfunctions and Effective Potentials -- 5 Benchmark Calculations of Helium Atom Ground State -- 6 Conclusion -- References -- A Symbolic Study of the Satellite Dynamics Subject to Damping Torques -- 1 Introduction -- 2 Equations of Motion -- 3 Equilibrium Orientations of Satellite -- 4 Conditions for the Existence of Equilibrium Orientations of the Satellite -- 5 Necessary and Sufficient Conditions of Asymptotic Stability of the Equilibrium Orientations of Satellite -- 6 Conclusion -- References -- Characteristic Set Method for Laurent Differential Polynomial Systems -- 1 Introduction -- 2 Laurent Polynomial Systems -- 2.1 Laurent Regular Chain. 2.2 Characteristic Set Method -- 2.3 Laurent Gröbner Basis and Minimal Decomposition -- 3 Differential Polynomial Systems -- 3.1 Laurent Regular Differential Chains -- 3.2 Decision of Univariate Laurent Regular Differential Polynomial -- References -- Sparse Polynomial Interpolation with Finitely Many Values for the Coefficients -- 1 Introduction -- 2 Univariate Polynomial Interpolation -- 2.1 Sparse Interpolation with Finitely Many Coefficients -- 2.2 The Sparse Interpolation Algorithm -- 2.3 The Rational Number Coefficients Case -- 3 Multivariate Polynomial Sparse Interpolation with Modified Kronecker Substitution -- 3.1 Find a Good Prime -- 3.2 A Deterministic Algorithm -- 3.3 Probabilistic Algorithm -- 4 Experimental Results -- 5 Conclusion -- References -- On Stationary Motions of the Generalized Kowalewski Gyrostat and Their Stability -- 1 Introduction -- 2 Formulation of the Problem -- 3 Finding the Stationary Solutions -- 3.1 Permanent Rotations -- 3.2 Equilibria -- 4 On Invariant Manifolds of Codimension 2 -- 5 On Stability of the Stationary Solutions -- 5.1 On Stability of the Permanent Rotations -- 5.2 On Stability of the Equilibria -- 6 Conclusion -- 7 Appendix -- References -- Computing the Integer Points of a Polyhedron, I: Algorithm -- 1 Introduction -- 2 Polyhedral Sets -- 3 Integer Solutions of Linear Equation Systems -- 4 Integer Solutions of Linear Inequality Systems -- 4.1 Normalization of Linear Inequality Systems -- 4.2 Representing the Integer Points -- 4.3 The IntegerSolve Procedure: Specifications -- 4.4 The DarkShadow Procedure -- 4.5 The GreyShadow Procedure -- 4.6 The IntegerSolve Procedure: Algorithm -- References -- Computing the Integer Points of a Polyhedron, II: Complexity Estimates -- 1 Introduction -- 2 Properties of the Projection of Faces of a Polyhedron -- 3 Complexity Estimates for Fourier-Motzkin Elimination. 4 Proof of Theorem1 -- 5 Experimentation -- References -- Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data -- 1 Problem Formulation -- 2 Non-Linearity of JTF and Numerical Difficulties -- 3 Non-Convexity of JTF -- 4 Numerical Experiments for Fitting Sparse Reduced Data -- 5 Conclusions -- References -- The Convergence Conditions of Interval Newton's Method Based on Point Estimates -- 1 Introduction -- 2 Notation and Preliminaries -- 3 Main Results -- 4 Example -- References -- Normalization of Indexed Differentials Based on Function Distance Invariants -- 1 Introduction -- 2 Indexed Differential Polynomial Ring -- 3 Distances Between Indexed Functions -- 4 Normalization with Respect to Monoterm Symmetries -- 5 Normalization -- References -- Symbolic-Numeric Integration of the Dynamical Cosserat Equations -- 1 Introduction -- 2 Governing Cosserat Equations and the General Solution of Their Kinematic Part -- 3 Symbolic-Numeric Integration Method -- 3.1 Naive Approach: Explicit Numerical Solving -- 3.2 Advanced Approach Based on Exponential Integration -- 4 Numerical Comparison with the Generalized alpha-Method -- 5 Conclusison -- A Generalized alpha-Method -- References -- Algorithms for Zero-Dimensional Ideals Using Linear Recurrent Sequences -- 1 Introduction -- 2 Generalities on Sequences and Their Annihilators -- 3 Computing Annihilators of Sequences -- 3.1 A First Algorithm -- 3.2 An Algorithm Under Genericity Assumptions -- 4 Main Algorithm -- 4.1 Representing Primary Zero-Dimensional Ideals -- 4.2 The Algorithm -- References -- Symbolic-Numerical Analysis of the Relative Equilibria Stability in the Planar Circular Restricted Four-Body Problem -- 1 Introduction -- 2 Equilibrium Solutions -- 3 Stability Analysis in Linear Approximation -- 4 Normalization of the Hamiltonian -- 5 Conclusion -- References. The Method of Collocations and Least Residuals Combining the Integral Form of Collocation Equations and the Matching Differential Relations at the Solution of PDEs. |
| Record Nr. | UNINA-9910483297903321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer Algebra in Scientific Computing [[electronic resource] ] : 18th International Workshop, CASC 2016, Bucharest, Romania, September 19-23, 2016, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing [[electronic resource] ] : 18th International Workshop, CASC 2016, Bucharest, Romania, September 19-23, 2016, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (XIII, 513 p. 61 illus.) |
| Disciplina | 004.0151 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Algorithms
Computer science—Mathematics Discrete mathematics Computer simulation Numerical analysis Computer arithmetic and logic units Discrete Mathematics in Computer Science Symbolic and Algebraic Manipulation Computer Modelling Numerical Analysis Arithmetic and Logic Structures |
| ISBN | 3-319-45641-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | On the Differential and Full Algebraic Complexities of Operator Matrices Transformations -- Resolving Decompositions for Polynomial Modules -- Setup of Order Conditions for Splitting Methods -- Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators -- Improved Computation of Involutive Bases -- Computing all Space Curve Solutions of Polynomial Systems by Polyhedral Methods -- Algorithmic Computation of Polynomial Amoebas -- Sparse Gaussian Elimination Modulo p: an Update -- MathCheck2: A SAT+CAS Verifier for Combinatorial Conjectures -- Incompleteness, Undecidability and Automated Proofs (Invited Talk) -- A Numerical Method for Computing Border Curves of Bi-Parametric Real Polynomial Systems and Applications -- The Complexity of Cylindrical Algebraic Decomposition with Respect to Polynomial Degree -- Efficient Simplification Techniques for Special Real Quantifier Elimination with Applications to the Synthesis of Optimal Numerical Algorithms -- Symbolic-Numeric Algorithms for Solving BVPs for a System of ODEs of the Second Order: Multichannel Scattering and Eigenvalue Problems -- Symbolic Algorithm for Generating Irreducible Rotational-Vibrational Bases of Point Groups -- A Symbolic Investigation of the Influence of Aerodynamic Forces on Satellite Equilibria -- Computer Algebra in High-Energy Physics (Invited Talk) -- A Note on Dynamic Gröbner Bases Computation -- Qualitative Analysis of the Reyman-Semenov-Tian-Shansky Integrable Case of the Generalized Kowalewski Top -- On Multiple Eigenvalues of a Matrix Dependent on a Parameter -- A Generalised Branch-and-Bound Approach and its Application in SAT Modulo Nonlinear Integer Arithmetic -- Computing Characteristic Polynomials of Matrices of Structured Polynomials -- Computing Sparse Representations of Systems of Rational Fractions -- On the General Analytical Solution of the Kinematic Cosserat Equations -- Using Sparse Interpolation in Hensel Lifting -- A Survey of Satisfiability Modulo Theory -- Quadric Arrangement in Classifying Rigid Motions of a 3D Digital Image -- A Lower Bound for Computing Lagrange's Real Root Bound -- Enhancing the Extended Hensel Construction by Using Gröbner Bases -- Symbolic-Numerical Optimization and Realization of the Method of Collocations and Least Residuals for Solving the Navier-Stokes Equations -- Pruning Algorithms for Pretropisms of Newton Polytopes -- Computational Aspects of a Bound of Lagrange. |
| Record Nr. | UNISA-996466272803316 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Computer Algebra in Scientific Computing : 18th International Workshop, CASC 2016, Bucharest, Romania, September 19-23, 2016, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing : 18th International Workshop, CASC 2016, Bucharest, Romania, September 19-23, 2016, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (XIII, 513 p. 61 illus.) |
| Disciplina | 004.0151 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Algorithms
Computer science—Mathematics Discrete mathematics Computer simulation Numerical analysis Computer arithmetic and logic units Discrete Mathematics in Computer Science Symbolic and Algebraic Manipulation Computer Modelling Numerical Analysis Arithmetic and Logic Structures |
| ISBN | 3-319-45641-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | On the Differential and Full Algebraic Complexities of Operator Matrices Transformations -- Resolving Decompositions for Polynomial Modules -- Setup of Order Conditions for Splitting Methods -- Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators -- Improved Computation of Involutive Bases -- Computing all Space Curve Solutions of Polynomial Systems by Polyhedral Methods -- Algorithmic Computation of Polynomial Amoebas -- Sparse Gaussian Elimination Modulo p: an Update -- MathCheck2: A SAT+CAS Verifier for Combinatorial Conjectures -- Incompleteness, Undecidability and Automated Proofs (Invited Talk) -- A Numerical Method for Computing Border Curves of Bi-Parametric Real Polynomial Systems and Applications -- The Complexity of Cylindrical Algebraic Decomposition with Respect to Polynomial Degree -- Efficient Simplification Techniques for Special Real Quantifier Elimination with Applications to the Synthesis of Optimal Numerical Algorithms -- Symbolic-Numeric Algorithms for Solving BVPs for a System of ODEs of the Second Order: Multichannel Scattering and Eigenvalue Problems -- Symbolic Algorithm for Generating Irreducible Rotational-Vibrational Bases of Point Groups -- A Symbolic Investigation of the Influence of Aerodynamic Forces on Satellite Equilibria -- Computer Algebra in High-Energy Physics (Invited Talk) -- A Note on Dynamic Gröbner Bases Computation -- Qualitative Analysis of the Reyman-Semenov-Tian-Shansky Integrable Case of the Generalized Kowalewski Top -- On Multiple Eigenvalues of a Matrix Dependent on a Parameter -- A Generalised Branch-and-Bound Approach and its Application in SAT Modulo Nonlinear Integer Arithmetic -- Computing Characteristic Polynomials of Matrices of Structured Polynomials -- Computing Sparse Representations of Systems of Rational Fractions -- On the General Analytical Solution of the Kinematic Cosserat Equations -- Using Sparse Interpolation in Hensel Lifting -- A Survey of Satisfiability Modulo Theory -- Quadric Arrangement in Classifying Rigid Motions of a 3D Digital Image -- A Lower Bound for Computing Lagrange's Real Root Bound -- Enhancing the Extended Hensel Construction by Using Gröbner Bases -- Symbolic-Numerical Optimization and Realization of the Method of Collocations and Least Residuals for Solving the Navier-Stokes Equations -- Pruning Algorithms for Pretropisms of Newton Polytopes -- Computational Aspects of a Bound of Lagrange. |
| Record Nr. | UNINA-9910483386803321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer Algebra in Scientific Computing [[electronic resource] ] : 17th International Workshop, CASC 2015, Aachen, Germany, September 14-18, 2015, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing [[electronic resource] ] : 17th International Workshop, CASC 2015, Aachen, Germany, September 14-18, 2015, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
| Descrizione fisica | 1 online resource (XIII, 494 p. 75 illus. in color.) |
| Disciplina | 005.1 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Algorithms
Computer science—Mathematics Discrete mathematics Computer arithmetic and logic units Discrete Mathematics in Computer Science Symbolic and Algebraic Manipulation Arithmetic and Logic Structures |
| ISBN | 3-319-24021-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Organization -- Contents -- Hypergeometric Solutions of First-Order Linear Difference Systems with Rational-Function Coefficients -- 1 Introduction -- 2 The Problem -- 3 The Reasoning Behind the Algorithm -- 3.1 The Resolving Equation and Matrix -- 3.2 The Minimal Subspace Containing All Solutions with yi=0 -- 3.3 The Use of RNF -- 3.4 The Space of Solutions with yi=0 -- 3.5 When k=m -- 3.6 Selection of yi -- 4 The Algorithm -- 5 On the Resolving Procedure -- 6 Implementation and Experiments -- 6.1 Implementation -- 6.2 Some Experiments -- 6.3 Comparison with the Cyclic Vector Approach -- Janet Bases and Resolutions in CoCoALib -- 1 Introduction -- 2 Involutive Bases and Free Resolutions -- 3 Free Resolutions with Janet Bases -- 4 Benchmarks -- Regular Chains under Linear Changesof Coordinates and Applications -- 1 Introduction -- 2 Preliminaries -- 3 Algorithm for Linear Change of Coordinates -- 4 Noether Normalization and Regular Chains -- 5 Applications of Random Linear Changes of Coordinates -- 6 On the Computation of lim(W(T)) and sat(T) -- 7 Conclusion -- A Standard Basis Free Algorithm for Computing the Tangent Cones of a Space Curve -- 1 Introduction -- 2 Preliminaries -- 2.1 Tangent Cone of a Space Curve -- 2.2 Regular Chains -- 3 Computing Intersection Multiplicities in Higher Dimension -- 4 Computing Tangent Lines as Limits of Secants -- 4.1 An Algorithmic Principle -- 4.2 Algorithm -- 4.3 Equations of Tangent Cones -- 4.4 Examples -- 5 Conclusion -- Research on the Stability of Relative Equilibria of Oblate Axisymmetric Gyrostat by Meansof Symbolic-Numerical Modelling -- 1 Introduction -- 2 Relative Equilibria -- 3 Construction of Symbolical Model and Parametrization of a Problem -- 4 Stability of the Third Class Equilibria -- 4.1 Necessary Conditions of Stability -- 4.2 Stable and Unstable Equilibria.
4.3 Gyroscopic Stabilization: Symbolic-Numerical Modelling -- 5 Parametrical Analysis of the Conditions of Gyroscopic Stabilization for Second Class Equilibria -- 6 Conclusion -- A New Approach for Computing Regular Solutions of Linear Difference Systems -- 1 Factorial Series -- 1.1 Definition -- 1.2 Ring Structure -- 1.3 Translation z z + -- 2 The Functions n -- 2.1 Definition -- 2.2 Properties -- 3 Regular Solutions of Linear Difference Systems -- 4 Appendix -- 4.1 Proof of Proposition 1 -- 4.2 Proof of Theorem 1 -- Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation -- 1 Introduction -- 2 Related Work and Alternative Approaches -- 3 Design and Implementation -- 4 Solving by Polynomial Homotopy Continuation -- 4.1 Running a Blackbox Solver -- 4.2 The Scripting Interface phcpy -- 5 Pattern Matching with a Database -- 5.1 The Classification Problem -- 5.2 The Graph Isomorphism Problem -- 5.3 Computing Canonical Graph Labelings With Nauty -- 5.4 Benchmarking the Canonization -- 5.5 Storing Labelings in a Database -- 6 Conclusions -- Finding First Integrals Using Normal Forms Modulo Differential Regular Chains -- 1 Introduction -- 2 Basis of Linear Dependences of Rational Functions -- 2.1 Preliminary Results -- 2.2 Algorithm findKernelBasis -- 2.3 A Variant of findKernelBasis -- 3 Incremental Computation of Linear Dependences -- 3.1 Algorithm incrementalFindDependence -- 3.2 Improvement Using a LU-decomposition -- 3.3 Finding the First Linear Dependence -- 3.4 Complexity of the Linear Algebra -- 4 Application to Finding First Integrals -- 4.1 Basic Differential Algebra -- 4.2 Normal Form Modulo a Differential Regular Chain -- 4.3 Normal Form Modulo a Decomposition -- 4.4 First Integrals in Differential Algebra -- 4.5 Algorithm findAllFirstIntegrals -- 4.6 Complexity -- Simplification of Cylindrical Algebraic Formulas. 1 Introduction -- 2 Preliminary -- 3 Motivating Examples -- 4 Algorithm -- 5 Experimentation -- 6 Conclusions -- Quasi-Steady State - Intuition, Perturbation Theory and Algorithmic Algebra -- 1 Introduction -- 2 Transferring Scientific to Mathematical Notions -- 3 Preliminaries and Notation -- 3.1 Lie Derivatives and Invariance Criteria -- 3.2 Singular Perturbations -- 4 The Ad Hoc Approach -- 5 Reduction in the SPT Setting -- 5.1 Conditions -- 5.2 Reduction of Rational Systems -- 5.3 Algorithmic Aspects -- 6 Identifying ``Small Parameters -- 6.1 Definition and Basic Properties -- 6.2 Structure of the TFPV Set -- 6.3 Algorithmic Aspects -- 7 The Ad Hoc Approach Revisited -- 7.1 Basics and Approximation Properties -- 7.2 Polynomial Systems and Algorithmic Aspects -- 8 Conclusion -- Polynomial Complexity Recognizing a Tropical Linear Variety -- Computing Highest-Order Divisors for a Classof Quasi-Linear Partial Differential Equations -- 1 Bound on a Degree of a Divisor -- 2 Algorithm to Find the Algebraic Variety of All the Divisors -- Symbolic Algorithm for Generating Irreducible Bases of Point Groups in the Space of SO(3) Group -- 1 Introduction -- 2 Rotations -- 2.1 Geometric Rotation -- 2.2 Rotation in Functional Spaces -- 3 Intrinsic Group -- 4 Generalized Projection Operators -- 5 Example of Using the Algorithm for the Octahedral Group -- 5.1 Construction of Elements of the Octahedral Group from Its Generators -- 5.2 Construction of Irreducible Representations of the Octahedral Group O in the Cartesian Bases -- 5.3 GPOs Implementation for Standard and Intrinsic Point Groups -- 6 Conclusion -- Symbolic-Numeric Solution of Boundary-Value Problems for the Schrödinger Equation Usingthe Finite Element Method: Scattering Problem and Resonance States -- 1 Introduction -- 2 Formulation of Boundary-Value Problems. 2.1 Scattering Problem: The Physical Asymptotic Solutions in Longitudinal Coordinates and the Scattering Matrix -- 3 Generation of Algebraic Problems -- 3.1 The Calculation Scheme for the Solution Matrix h=h -- 3.2 The Calculation Scheme for the Solution Matrix h=h -- 3.3 Algorithm for Calculating the Complex Eigenvalues and Eigenfunctions of Metastable States -- 4 Benchmark Calculations -- 5 Conclusion -- Application of Computer Algebra Methodsto Investigation of Influence of Constant Torque on Stationary Motions of Satellite -- 1 Introduction -- 2 Equations of Motion -- 3 Equilibrium Orientations -- 4 Conclusion -- Bounds for the Condition Number of Polynomials Systems with Integer Coefficients -- 1 Introduction -- 1.1 Our Results -- 1.2 Notation -- 2 Condition Number for Univariate Polynomials -- 3 Condition Number for Polynomial Systems -- 3.1 Multivariate Aggregate Condition Number -- On Invariant Manifolds and Their Stabilityin the Problem of Motion of a Rigid Bodyunder the Influence of Two Force Fields -- 1 Introduction -- 2 Formulation of the Problem -- 3 Finding Invariant Manifolds -- 3.1 Finding the Invariant Manifolds Embedded in One Another -- 3.2 Finding the Enveloping Invariant Manifolds -- 3.3 On Invariant Manifolds under Restrictions on the Constantsof the Problem Integrals -- 4 On the Stability of Stationary Invariant Manifolds -- 5 Conclusion -- Homotopy Analysis Method for StochasticDifferential Equations with Maxima -- 1 Introduction -- 2 The Model -- 3 Homotopy Analysis Method -- 4 Homotopy Analysis Method and Stochastic Differential Equation with Third-Order Nonlinearity -- 5 Concluding Remarks -- On the Topology and Visualization of Plane Algebraic Curves -- 1 Introduction -- 2 Topology Computation for Plane Algebraic Curves -- 2.1 Solving the System {f=fy=0} -- 2.2 Computing the Fibers. 2.3 Branch Number Computation and Connection -- 3 Isotopic Meshing for a Plane Curve -- 3.1 Tracing Regular Curve Segments -- 3.2 Error Control for the Meshing of a Plane Curve -- 4 Experiments -- 5 Conclusions -- Piecewise-Quadratics and Reparameterizations for Interpolating Reduced Data -- 1 Introduction -- 2 Problem Formulation and Motivation -- 3 Main Result -- 4 Experiments -- 5 Conclusions -- Parametric Solvable Polynomial Rings and Applications -- 1 Introduction -- 1.1 Related Work -- 1.2 Outline -- 2 Solvable Polynomial Rings -- 2.1 Parametric Solvable Polynomial Rings -- 2.2 Solvable Polynomial Coefficient Rings -- 2.3 Recursive Solvable Polynomial Rings -- 2.4 Solvable Quotient and Residue Rings -- 2.5 Solvable Quotient Rings as Coefficient Rings -- 3 Implementation of Solvable Polynomial Rings -- 3.1 Polynomial Rings -- 3.2 Solvable Polynomial Rings -- 3.3 Recursive Solvable Polynomial Rings -- 3.4 Solvable Quotient and Residue Rings -- 3.5 Solvable Polynomial Rings with Non-commutative Coefficients -- 4 Applications -- 4.1 Comprehensive Gröbner Bases -- 4.2 Gröbner Bases and Applications -- 4.3 Examples -- 4.4 Extension to Free Non-commutative Coefficients -- 5 Conclusions -- Triangular Decomposition of Matrices in a Domain -- 1 Introduction -- 2 Preliminary. Triangular Decomposition in Domain -- 2.1 LDU Algorithm for the Matrix with Nonzero Diagonal Minors Up to the Rank -- 3 Triangular Matrix Decomposition -- 4 LDU Algorithm with Permutation Matrices -- 4.1 Left Upper Block A Is Not Zero Block -- 4.2 Matrix A Has Full Rank, Matrices C and (or) B Are Zero Matrices -- 4.3 Matrix A Has No Full Rank, Matrices C and (or) B Are Zero Matrices, A =0 -- 5 Matrix A is Zero Matrix -- 5.1 Matrix A Is Zero Matrix, C and (or) B Are Nonzero Matrices -- 5.2 All Cases When Half of the Matrix Is Equal to Zero. 6 Example of Triangular Decomposition on Z. |
| Record Nr. | UNISA-996466451203316 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Computer Algebra in Scientific Computing : 17th International Workshop, CASC 2015, Aachen, Germany, September 14-18, 2015, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing : 17th International Workshop, CASC 2015, Aachen, Germany, September 14-18, 2015, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
| Descrizione fisica | 1 online resource (XIII, 494 p. 75 illus. in color.) |
| Disciplina | 005.1 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Algorithms
Computer science—Mathematics Discrete mathematics Computer arithmetic and logic units Discrete Mathematics in Computer Science Symbolic and Algebraic Manipulation Arithmetic and Logic Structures |
| ISBN | 3-319-24021-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Organization -- Contents -- Hypergeometric Solutions of First-Order Linear Difference Systems with Rational-Function Coefficients -- 1 Introduction -- 2 The Problem -- 3 The Reasoning Behind the Algorithm -- 3.1 The Resolving Equation and Matrix -- 3.2 The Minimal Subspace Containing All Solutions with yi=0 -- 3.3 The Use of RNF -- 3.4 The Space of Solutions with yi=0 -- 3.5 When k=m -- 3.6 Selection of yi -- 4 The Algorithm -- 5 On the Resolving Procedure -- 6 Implementation and Experiments -- 6.1 Implementation -- 6.2 Some Experiments -- 6.3 Comparison with the Cyclic Vector Approach -- Janet Bases and Resolutions in CoCoALib -- 1 Introduction -- 2 Involutive Bases and Free Resolutions -- 3 Free Resolutions with Janet Bases -- 4 Benchmarks -- Regular Chains under Linear Changesof Coordinates and Applications -- 1 Introduction -- 2 Preliminaries -- 3 Algorithm for Linear Change of Coordinates -- 4 Noether Normalization and Regular Chains -- 5 Applications of Random Linear Changes of Coordinates -- 6 On the Computation of lim(W(T)) and sat(T) -- 7 Conclusion -- A Standard Basis Free Algorithm for Computing the Tangent Cones of a Space Curve -- 1 Introduction -- 2 Preliminaries -- 2.1 Tangent Cone of a Space Curve -- 2.2 Regular Chains -- 3 Computing Intersection Multiplicities in Higher Dimension -- 4 Computing Tangent Lines as Limits of Secants -- 4.1 An Algorithmic Principle -- 4.2 Algorithm -- 4.3 Equations of Tangent Cones -- 4.4 Examples -- 5 Conclusion -- Research on the Stability of Relative Equilibria of Oblate Axisymmetric Gyrostat by Meansof Symbolic-Numerical Modelling -- 1 Introduction -- 2 Relative Equilibria -- 3 Construction of Symbolical Model and Parametrization of a Problem -- 4 Stability of the Third Class Equilibria -- 4.1 Necessary Conditions of Stability -- 4.2 Stable and Unstable Equilibria.
4.3 Gyroscopic Stabilization: Symbolic-Numerical Modelling -- 5 Parametrical Analysis of the Conditions of Gyroscopic Stabilization for Second Class Equilibria -- 6 Conclusion -- A New Approach for Computing Regular Solutions of Linear Difference Systems -- 1 Factorial Series -- 1.1 Definition -- 1.2 Ring Structure -- 1.3 Translation z z + -- 2 The Functions n -- 2.1 Definition -- 2.2 Properties -- 3 Regular Solutions of Linear Difference Systems -- 4 Appendix -- 4.1 Proof of Proposition 1 -- 4.2 Proof of Theorem 1 -- Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation -- 1 Introduction -- 2 Related Work and Alternative Approaches -- 3 Design and Implementation -- 4 Solving by Polynomial Homotopy Continuation -- 4.1 Running a Blackbox Solver -- 4.2 The Scripting Interface phcpy -- 5 Pattern Matching with a Database -- 5.1 The Classification Problem -- 5.2 The Graph Isomorphism Problem -- 5.3 Computing Canonical Graph Labelings With Nauty -- 5.4 Benchmarking the Canonization -- 5.5 Storing Labelings in a Database -- 6 Conclusions -- Finding First Integrals Using Normal Forms Modulo Differential Regular Chains -- 1 Introduction -- 2 Basis of Linear Dependences of Rational Functions -- 2.1 Preliminary Results -- 2.2 Algorithm findKernelBasis -- 2.3 A Variant of findKernelBasis -- 3 Incremental Computation of Linear Dependences -- 3.1 Algorithm incrementalFindDependence -- 3.2 Improvement Using a LU-decomposition -- 3.3 Finding the First Linear Dependence -- 3.4 Complexity of the Linear Algebra -- 4 Application to Finding First Integrals -- 4.1 Basic Differential Algebra -- 4.2 Normal Form Modulo a Differential Regular Chain -- 4.3 Normal Form Modulo a Decomposition -- 4.4 First Integrals in Differential Algebra -- 4.5 Algorithm findAllFirstIntegrals -- 4.6 Complexity -- Simplification of Cylindrical Algebraic Formulas. 1 Introduction -- 2 Preliminary -- 3 Motivating Examples -- 4 Algorithm -- 5 Experimentation -- 6 Conclusions -- Quasi-Steady State - Intuition, Perturbation Theory and Algorithmic Algebra -- 1 Introduction -- 2 Transferring Scientific to Mathematical Notions -- 3 Preliminaries and Notation -- 3.1 Lie Derivatives and Invariance Criteria -- 3.2 Singular Perturbations -- 4 The Ad Hoc Approach -- 5 Reduction in the SPT Setting -- 5.1 Conditions -- 5.2 Reduction of Rational Systems -- 5.3 Algorithmic Aspects -- 6 Identifying ``Small Parameters -- 6.1 Definition and Basic Properties -- 6.2 Structure of the TFPV Set -- 6.3 Algorithmic Aspects -- 7 The Ad Hoc Approach Revisited -- 7.1 Basics and Approximation Properties -- 7.2 Polynomial Systems and Algorithmic Aspects -- 8 Conclusion -- Polynomial Complexity Recognizing a Tropical Linear Variety -- Computing Highest-Order Divisors for a Classof Quasi-Linear Partial Differential Equations -- 1 Bound on a Degree of a Divisor -- 2 Algorithm to Find the Algebraic Variety of All the Divisors -- Symbolic Algorithm for Generating Irreducible Bases of Point Groups in the Space of SO(3) Group -- 1 Introduction -- 2 Rotations -- 2.1 Geometric Rotation -- 2.2 Rotation in Functional Spaces -- 3 Intrinsic Group -- 4 Generalized Projection Operators -- 5 Example of Using the Algorithm for the Octahedral Group -- 5.1 Construction of Elements of the Octahedral Group from Its Generators -- 5.2 Construction of Irreducible Representations of the Octahedral Group O in the Cartesian Bases -- 5.3 GPOs Implementation for Standard and Intrinsic Point Groups -- 6 Conclusion -- Symbolic-Numeric Solution of Boundary-Value Problems for the Schrödinger Equation Usingthe Finite Element Method: Scattering Problem and Resonance States -- 1 Introduction -- 2 Formulation of Boundary-Value Problems. 2.1 Scattering Problem: The Physical Asymptotic Solutions in Longitudinal Coordinates and the Scattering Matrix -- 3 Generation of Algebraic Problems -- 3.1 The Calculation Scheme for the Solution Matrix h=h -- 3.2 The Calculation Scheme for the Solution Matrix h=h -- 3.3 Algorithm for Calculating the Complex Eigenvalues and Eigenfunctions of Metastable States -- 4 Benchmark Calculations -- 5 Conclusion -- Application of Computer Algebra Methodsto Investigation of Influence of Constant Torque on Stationary Motions of Satellite -- 1 Introduction -- 2 Equations of Motion -- 3 Equilibrium Orientations -- 4 Conclusion -- Bounds for the Condition Number of Polynomials Systems with Integer Coefficients -- 1 Introduction -- 1.1 Our Results -- 1.2 Notation -- 2 Condition Number for Univariate Polynomials -- 3 Condition Number for Polynomial Systems -- 3.1 Multivariate Aggregate Condition Number -- On Invariant Manifolds and Their Stabilityin the Problem of Motion of a Rigid Bodyunder the Influence of Two Force Fields -- 1 Introduction -- 2 Formulation of the Problem -- 3 Finding Invariant Manifolds -- 3.1 Finding the Invariant Manifolds Embedded in One Another -- 3.2 Finding the Enveloping Invariant Manifolds -- 3.3 On Invariant Manifolds under Restrictions on the Constantsof the Problem Integrals -- 4 On the Stability of Stationary Invariant Manifolds -- 5 Conclusion -- Homotopy Analysis Method for StochasticDifferential Equations with Maxima -- 1 Introduction -- 2 The Model -- 3 Homotopy Analysis Method -- 4 Homotopy Analysis Method and Stochastic Differential Equation with Third-Order Nonlinearity -- 5 Concluding Remarks -- On the Topology and Visualization of Plane Algebraic Curves -- 1 Introduction -- 2 Topology Computation for Plane Algebraic Curves -- 2.1 Solving the System {f=fy=0} -- 2.2 Computing the Fibers. 2.3 Branch Number Computation and Connection -- 3 Isotopic Meshing for a Plane Curve -- 3.1 Tracing Regular Curve Segments -- 3.2 Error Control for the Meshing of a Plane Curve -- 4 Experiments -- 5 Conclusions -- Piecewise-Quadratics and Reparameterizations for Interpolating Reduced Data -- 1 Introduction -- 2 Problem Formulation and Motivation -- 3 Main Result -- 4 Experiments -- 5 Conclusions -- Parametric Solvable Polynomial Rings and Applications -- 1 Introduction -- 1.1 Related Work -- 1.2 Outline -- 2 Solvable Polynomial Rings -- 2.1 Parametric Solvable Polynomial Rings -- 2.2 Solvable Polynomial Coefficient Rings -- 2.3 Recursive Solvable Polynomial Rings -- 2.4 Solvable Quotient and Residue Rings -- 2.5 Solvable Quotient Rings as Coefficient Rings -- 3 Implementation of Solvable Polynomial Rings -- 3.1 Polynomial Rings -- 3.2 Solvable Polynomial Rings -- 3.3 Recursive Solvable Polynomial Rings -- 3.4 Solvable Quotient and Residue Rings -- 3.5 Solvable Polynomial Rings with Non-commutative Coefficients -- 4 Applications -- 4.1 Comprehensive Gröbner Bases -- 4.2 Gröbner Bases and Applications -- 4.3 Examples -- 4.4 Extension to Free Non-commutative Coefficients -- 5 Conclusions -- Triangular Decomposition of Matrices in a Domain -- 1 Introduction -- 2 Preliminary. Triangular Decomposition in Domain -- 2.1 LDU Algorithm for the Matrix with Nonzero Diagonal Minors Up to the Rank -- 3 Triangular Matrix Decomposition -- 4 LDU Algorithm with Permutation Matrices -- 4.1 Left Upper Block A Is Not Zero Block -- 4.2 Matrix A Has Full Rank, Matrices C and (or) B Are Zero Matrices -- 4.3 Matrix A Has No Full Rank, Matrices C and (or) B Are Zero Matrices, A =0 -- 5 Matrix A is Zero Matrix -- 5.1 Matrix A Is Zero Matrix, C and (or) B Are Nonzero Matrices -- 5.2 All Cases When Half of the Matrix Is Equal to Zero. 6 Example of Triangular Decomposition on Z. |
| Record Nr. | UNINA-9910484288403321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer Algebra in Scientific Computing [[electronic resource] ] : 16th International Workshop, CASC 2014, Warsaw, Poland, September 8-12, 2014. Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing [[electronic resource] ] : 16th International Workshop, CASC 2014, Warsaw, Poland, September 8-12, 2014. Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 |
| Descrizione fisica | 1 online resource (XIV, 502 p. 73 illus.) |
| Disciplina | 512.00285 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Algorithms
Computer science—Mathematics Discrete mathematics Computer graphics Numerical analysis Computer arithmetic and logic units Discrete Mathematics in Computer Science Symbolic and Algebraic Manipulation Computer Graphics Numerical Analysis Arithmetic and Logic Structures |
| ISBN | 3-319-10515-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Relation Algebra, RelView, and Plurality Voting -- An Algorithm for Converting Nonlinear Differential Equations to Integral Equations with an Application to Parameter Estimation from Noisy Data -- Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains -- Computing the Topology of an Arrangement of Implicit and Parametric Curves Given by Values -- Finding a Deterministic Generic Position for an Algebraic Space Curve -- Computer Algebra Experimentation -- On the Parallelization of Subproduct Tree Techniques Targeting -- Many-core Architectures -- Deterministically Computing Reduction Numbers of Polynomial Ideals. |
| Record Nr. | UNISA-996202526503316 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Computer Algebra in Scientific Computing : 16th International Workshop, CASC 2014, Warsaw, Poland, September 8-12, 2014. Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing : 16th International Workshop, CASC 2014, Warsaw, Poland, September 8-12, 2014. Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 |
| Descrizione fisica | 1 online resource (XIV, 502 p. 73 illus.) |
| Disciplina | 512.00285 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Algorithms
Computer science—Mathematics Discrete mathematics Computer graphics Numerical analysis Computer arithmetic and logic units Discrete Mathematics in Computer Science Symbolic and Algebraic Manipulation Computer Graphics Numerical Analysis Arithmetic and Logic Structures |
| ISBN | 3-319-10515-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Relation Algebra, RelView, and Plurality Voting -- An Algorithm for Converting Nonlinear Differential Equations to Integral Equations with an Application to Parameter Estimation from Noisy Data -- Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains -- Computing the Topology of an Arrangement of Implicit and Parametric Curves Given by Values -- Finding a Deterministic Generic Position for an Algebraic Space Curve -- Computer Algebra Experimentation -- On the Parallelization of Subproduct Tree Techniques Targeting -- Many-core Architectures -- Deterministically Computing Reduction Numbers of Polynomial Ideals. |
| Record Nr. | UNINA-9910484397103321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
